Method for indicating fatigue damage of a metal object

ABSTRACT

A method for indicating fatigue damage rate of a hardened metal object in relation to load cycles, N, exerted on the hardened metal object, wherein the hardened metal object presents a temperature essentially corresponding to the operating conditions of the hardened metal object is disclosed. It comprises calculating the fatigue rate based on an effective activation energy parameter for the dislocation climb process, Q, shear stress amplitude, T, the absolute local temperature of the hardened metal object, T, and load frequency, f. Methods for indicating fatigue and predicting life of a metal object are disclosed.

TECHNICAL FIELD

The invention concerns methods of indicating fatigue damage and damagerate of a metal object, especially a hardened metal object, and inparticular a hardened metal bearing component.

BACKGROUND

Fatigue, one of the most common material degradation mechanisms inindustry in general and in the bearing industry in particular, occurswhen material experiences lengthy periods under repeated or cyclicstresses which can lead to failure at stress levels much lower than thetensile or yield strength. It has long been recognised that nearly 90%of industrial component failure takes place due to fatigue. Hence theimportance of evaluation of fatigue damage in metallic components andbuilding a solid understanding of the fatigue phenomenon, aiming atpreventing fatigue failures from occurring.

One example in this direction is EP1184813A2. EP1184813A2 describes howa dynamic equivalent load P is calculated from data information of arolling bearing. Thereafter, a reliability coefficient a_(l) isdetermined, a lubrication parameter a_(L) corresponding to a usedlubricant is calculated, and a contamination degree coefficient a_(c) isdetermined in consideration of a material coefficient. A fatigue limitload P_(u) is calculated on the basis of the data information.Thereafter, a load parameter {(P−P_(u))/C}·1/a_(o) is calculated. On thebasis of the lubrication parameter and the load parameter{(P−P_(u))/C}·1/a_(o), a life correction coefficient a_(NSK) iscalculated with reference to a life correction coefficient calculationmap. The bearing life L_(A) is calculated asL_(A)=a_(l)·a_(NSK)·(C/P)^(P).

Unfortunately life models commonly approach the fatigue problem in asimplified manner and commonly treat the metal in a highly idealisedway. The models therefore exhibit limitations and there seems still tobe room for improvements as regards the understanding of thecharacteristics of metals, especially as a bearing material, the lifemodels, and the influences from the operating environment on thecharacteristics of bearing material.

SUMMARY

According to one aspect, the present invention relates to a method forindicating fatigue damage rate of a hardened metal object and inparticular a hardened metal bearing component.

According to another aspect, the present invention relates to a methodfor indicating fatigue damage of a hardened metal object and inparticular a hardened metal bearing component.

According to still another aspect, the present invention relates to amethod for indicating at least one of an effective activation energyparameter for the dislocation climb process, shear stress amplitude, theabsolute temperature of the hardened metal object, load frequency, andnumber of load cycles exerted on the hardened metal object.

According to a further aspect, the present invention relates to acomputer program product implementing at least one of the previousaspects.

According to still a further aspect, the present invention relates to acomputer readable medium containing program instructions according toany of the previous aspects.

The present invention has its basis in a metal physics description ofhow hardened metal materials behave under high cycle fatigue conditions,including not only the effects of the Hertzian contact stress field, butalso the effects of the operating temperature, superimposed (hoop andresidual) stresses and speed. The term fatigue includes at least one ofrolling contact fatigue (RCF) and structural fatigue, such as rotatingbending fatigue, torsion fatigue, uniaxial fatigue, including push-pullfatigue, and multiaxial fatigue. The present invention deals withplastic damage rate, accumulated fatigue damage, cumulative fatigue,strain damage, and cumulative strain damage.

According to an aspect of the invention a method for indicating fatiguedamage rate of a hardened metal object in relation to load cycles, N,exerted on the hardened metal object, wherein the hardened metal objectpresents a temperature essentially corresponding to the operatingconditions of the hardened metal object is disclosed. It comprisescalculating the fatigue rate based on an effective activation energyparameter for the dislocation climb process, Q, shear stress amplitude,T, the absolute local temperature of the hardened metal object, T, andload frequency, f. Further also methods for indicating fatigue andpredicting life of a metal object are disclosed

According to one aspect of the present invention, a method forindicating fatigue damage rate of a hardened metal object in relation toload cycles, N, exerted on the hardened metal object will now bedisclosed. The hardened metal object has a local temperature. Localtemperature is here defined as a temperature essentially correspondingto the operating conditions of the hardened metal object. The methodcomprises calculating the fatigue damage rate on a load cycle base dγ/dNor a time base by using an alternative formalism, which will be furtherelaborated below. The calculating is based on an effective activationenergy parameter for the dislocation climb process, Q, shear stressamplitude, T (expressed in Pa), the absolute local temperature of thehardened metal object, T, and load frequency or rotational speed, f. Inan embodiment the load frequency is constant. In another embodiment, theload frequency varies over time. In an embodiment, the fatigue damagerate is indicated to a user. Each one of the shear stress amplitude andthe temperature are constant or variable over time.

In an embodiment, and in case of the shear stress and/or temperature isconstant or non-constant, the fatigue damage rate may be expressed asdγ/dt=A<T−T _(u)>^(c) e^((−kQ/RT)), where

-   -   A is A₀ (H_(Vref)/H_(V))^(d), where A₀ is a constant larger than        zero but smaller than 10⁻⁸, H_(Vref) is the Vickers hardness for        a reference metal, H_(V) is the Vickers hardness for the        hardened metal object,    -   <T−T _(u)> is zero for T≦T _(u) and T−T _(u) for T>T _(u), where        T _(u) is the fatigue limit for the hardened metal object,    -   c is a constant in the interval 6 to 22,    -   d is a constant in the interval 6 to 22,    -   k is a constant between 0.50 and 1.50,    -   T is the absolute temperature of the hardened metal object at        the point of contact, and    -   R is the universal gas constant.

However, substituting t=N/f in the expression above (and thusdt=(1/f)dN), an embodiment is reached, in which the step of calculatingcomprises calculating dγ/dN according to

dγ/dN=A< T−T _(u)>^(c) e ^((−kQ/RT)) /f, where

-   -   A is A₀(H_(Vref)/H_(V))^(d), where A₀ is a constant larger than        zero but smaller than 10⁻⁸, H_(Vref) is the Vickers hardness for        a reference metal, H_(V) is the Vickers hardness for the        hardened metal object    -   <T−T _(u)> is zero for T≦T _(u) and T−T _(u) for T>T _(u), where        T _(u) is the fatigue limit for the hardened metal object,    -   c is a constant in the interval 6 to 22,    -   d is a constant in the interval 6 to 22,    -   k is a constant between 0.50 and 1.50,    -   T is the absolute temperature of the hardened metal object at        the point of contact, and    -   R is the universal gas constant.

In an embodiment, the absolute temperature T expressed in degreesCelsius, t, is in the interval of −55 to 250 degrees Celsius, wheret=T−To and To=273.15 degrees Kelvin. In other embodiments thetemperature, t, is in the interval of zero to 250 degrees Celsius, inthe interval of 15 to 200 degrees Celsius, in the interval of 30 to 150degrees Celsius, in the interval of 50 to 120 degrees Celsius, in theinterval 65 to 110 degrees Celsius, or in the interval 75 to 100 degreesCelsius. In some embodiments, the absolute temperature, T, of thehardened metal object is below 0.4T_(m), where T_(m) is the absolutemelting temperature of the hardened metal object.

In some embodiments, the method further comprises calculating theeffective activation energy parameter for the dislocation climb process,Q, according to Q=Q₀−ΔVσ, where ΔV is a material constant, and σ is thenormal stress field tensor. According to the invention it has also beendetermined that the fatigue damage process is also influenced by thesuperimposed (static or dynamic) normal stress field. In otherembodiments, σ is the hydrostatic stress, which in an embodiment, iscalculated according to: σ=(σ_(xx)+σ_(yy)+σ_(zz))/3, where σ_(xx),σ_(yy), σ_(zz) are the normal stress components.

In another aspect of the invention, integrating the fatigue damage raterelation according to the first aspect over time, or more specificallythe variable of number of load cycles, using the actual operatingconditions, gives the cumulative fatigue damage, i.e. the integral ofthe first aspect. A method for indicating cumulative fatigue damage, γ,of a hardened metal object at a temperature essentially corresponding tothe local operating conditions of the hardened metal object and underconstant stress amplitude will now be disclosed. It comprisescalculating the cumulative fatigue damage, γ, based on effectiveactivation energy parameter for the dislocation climb process, Q, shearstress amplitude, T, the absolute local temperature of the hardenedmetal object, T, load frequency, or rotational speed, f, and number ofload cycles, N, exerted on the hardened metal object.

In a case of the shear stress and temperature being constant, thefatigue damage may be expressed as γ=A<T−T _(u)>^(c)e^((−kQ/RT))t. Thisis the integral of the expression concerning the time based fatiguedamage rate discussed above.

However, using also, for a constant load frequency, the substitutiont=N/f, an embodiment is reached, in which the step of calculatingcomprises calculating γ according to:

γ=A> T−T _(u)>^(c) e ^((−kQ/RT)) N/f, where

-   -   A is A₀(H_(Vref)/H_(V))^(d), where A₀ is a constant larger than        zero but smaller than 10⁻⁸, H_(Vref) is the Vickers hardness for        a reference metal, H_(V) is the Vickers hardness for the        hardened metal object,    -   <T−T _(u)> is zero for T≦T _(u) and T−T _(u) for T>T _(u), where        T _(u) is the fatigue limit for the hardened metal object,    -   c is a constant in the interval 6 to 22,    -   d is a constant in the interval 6 to 22,    -   k is a constant between 0.50 and 1.50,    -   T is the absolute temperature of the hardened metal object at        the point of contact, and    -   R is the universal gas constant.

In some embodiments, the absolute temperature T expressed in degreesCelsius, t, is in the interval of −55 to 250 degrees Celsius, in theinterval of zero to 250 degrees Celsius, in the interval of 15 to 200degrees Celsius, in the interval of 30 to 150 degrees Celsius, in theinterval of 50 to 120 degrees Celsius, in the interval 65 to 110 degreesCelsius, or in the interval 75 to 100 degrees Celsius, where t=T−To andTo=273.15 degrees Kelvin. In other embodiments, the temperature, T, isbelow 0.4T_(m), where T_(m) is the absolute melting temperature of thehardened metal object.

In some embodiments, the method further comprises calculating theeffective activation energy parameter for the dislocation climb process,Q, according to Q=Q₀−ΔVσ, where ΔV is a material constant, and σ is thenormal stress field tensor. This is due to that the fatigue damageprocess is also influenced by the superimposed (static or dynamic)normal stress field. In some embodiments, σ is the hydrostatic stress,and in other embodiments, σ is calculated according toσ=(σ_(xx)+σ_(yy)+σ_(zz))/3, where σ_(xx), σ_(yy), σ_(zz) are the normalstress components.

Now turning to still another aspect and assuming that metal failureoccurs when the highest stressed point has accumulated a (non-specified)critical degree of plastic damage, then the formula presented in thesecond aspect may be used to predict the metal fatigue life. Accordingto this aspect, a method for indicating at least one of an effectiveactivation energy parameter for the dislocation climb process, Q, shearstress amplitude, T, the absolute local temperature of the hardenedmetal object, T, load frequency or rotational speed, f, and number ofload cycles, N, exerted on the hardened metal object, at a temperatureessentially corresponding to the operating conditions of the hardenedmetal object and under constant stress amplitude is disclosed. In anembodiment, the method may also be used to indicate normal stress fieldor hydrostatic stress. The method is based on the following relation

N=Cf/(<T−T _(u)>^(c) e ^((−kQ/RT))), where

-   -   C=C₀ (H_(V)/H_(Vref))^(d), where C₀ is a calibration constant        representing operating conditions for a reference metal object        having a known fatigue life in terms of estimated maximum number        of load cycles, H_(Vref) is the Vickers hardness for a reference        metal and H_(V) is the Vickers hardness for the hardened metal        object,    -   <T−T _(u)> is zero for T≦T _(u) and T−T _(u) for T>T _(u), where        T _(u) is the fatigue limit for the hardened metal object,    -   c is a constant in the interval 6 to 22,    -   d is a constant in the interval 6 to 22,    -   k is a constant between 0.50 and 1.50,    -   T is the absolute temperature of the hardened metal object at        the point of contact, and    -   R is the universal gas constant.

Thus, C₀ is a constant that represents the reference operatingconditions for the metal object having a known life (for example fromendurance testing) and which was used to calibrate the model.

The industrial applicability of the formula above is of course notlimited to estimating N, but, for instance when a prediction of N may beknown before hand, to solve the equation in view of for instance thelocal temperature.

In some embodiments, the absolute temperature T expressed in degreesCelsius, t, is in the interval of −55 to 250 degrees Celsius, in theinterval of zero to 250 degrees Celsius, in the interval of 15 to 200degrees Celsius, in the interval of 30 to 150 degrees Celsius, in theinterval of 50 to 120 degrees Celsius, in the interval 65 to 110 degreesCelsius, or in the interval 75 to 110 degrees Celsius, where t=T−To andTo=273.15 degrees Kelvin. In other embodiments, the temperature, T, isbelow 0.4T_(m), where T_(m) is the absolute melting temperature of thehardened metal object.

In some embodiments, the method further comprises calculating theeffective activation energy parameter for the dislocation climb process,Q, according to Q=Q₀−ΔVσ, where ΔV is a material constant, and σ is thenormal stress field.

This is due to that the fatigue damage process is also influenced by thesuperimposed (static or dynamic) normal stress field.

In some embodiments, σ is the hydrostatic stress, and in otherembodiments, it is calculated according to σ=(σ_(xx)+σ_(yy)+σ_(zz))/3,where σ_(xx), σ_(yy), σ_(zz) are the normal stress components.

According to a further aspect, a computer program product is disclosed.It is loadable into the internal memory of a computer, comprisingsoftware code portions for performing step(s) of any of the previousaspects, when run on a computer.

According to still a further aspect, a computer readable mediumcontaining program instructions for execution on a computer system,which when executed by the computer system, cause the computer system toperform step(s) of any of the previous aspects.

In a non-limiting embodiment the aspects of the present invention may beutilised in remote control, or remote monitoring, of machinerycomprising hardened materials by measuring and monitoring the variablesdiscussed above.

The different enhancements of the invention as described above can becombined in any desired manner as long as no conflictingenhancements/features/characteristics are combined.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will now be described in more detail for explanatory, andin no sense limiting, purposes, with reference to the following figures,in which

FIG. 1 shows a schematic illustration of a device suitable for executingthe methods according to present invention,

FIG. 2 shows a schematic illustration of a fatigue test rig,

FIG. 3-5 shows diagrams indicating the relation between fatigue damage,in terms of surface groove depth, number of load cycles, and theabsolute temperature of the hardened metal object.

DETAILED DESCRIPTION

In order to clarify the method and device according to the invention,some examples of its use will now be described in connection with FIGS.1 to 5.

High cycle fatigue response can be seen as being a function of theapplied stress amplitude and the number of stress cycles, i.e. amechanical approach. The fatigue life is then to some extent seen as aprobabilistic process that can be treated using statistical methods.Correction factors for any applied mean stress, lubricant film thicknessand lubricant contamination are then applied in metal life models forrolling contact fatigue (RCF). The relationship between the appliedbearing load (P) and the life (L), expressed in million revolutions, hasthe form:

L=a _(SLF)(C/P)^(p)≈Constant/<T−T _(u)>^(c),

where a_(SLF) is the stress life factor, C is the basic dynamic loadrating, p is the load ratio exponent, T is the subsurface shear stressamplitude, T _(u) is a fatigue limit shear stress and c is the shearstress exponent. Here <T−T _(u)> is zero for T≦T _(u) and T−T _(u) forT>T _(u). However, it should be noted that this does not treat fatiguedamage as being a microstructural effect and therefore only describesthe material rather as being a “continuum” having predefined (andnon-changing) properties. Still metallographic techniques, includingmicroscopy and X-ray diffraction methods can be used to monitor theaccumulation of fatigue damage in mechanical objects, such as bearings.This is an implicit use of a changing microstructure in relation to thefatigue exposure, without detailing how these changes come about.

Some metal life models approach the fatigue problem from a purelymechanical perspective and treats the metal in a highly idealised way.These models therefore exhibit limitations as regards the description ofinfluences from the operating environment on the characteristics of thebearing material.

A fundamental aspect of the invention is the understanding that duringfatigue, the microstructure of materials experiences continuous changesuntil failure.

According to the invention, by introducing a better materialdescription, further improved predictability power of models can beachieved. Such improved models can be used to better dimension metalobjects, e.g. bearings, for adverse operating conditions likeenvironmental influences or combined high load and temperature leadingto marginal lubrication conditions. By including additional influencingoperating parameters like temperature, internal stress state and speed,improved predictability of e.g. life of mechanical objects, is provided.

According to the invention, fatigue damage is seen as a cumulativesmall-scale plastic deformation process, being controlled by a thermallyactivated dislocation climb process. The damage induced is a result of asecondary creep-like dislocation process, where iron self-diffusioncontrolled climb constitutes the rate controlling step, while the majorpart of the damage induced is a result of dislocation glide, once thedislocations are freed from the obstacles via the climb process(climb+glide). The damage process is therefore driven by the appliedshear stress field and is rate controlled via diffusion-controlledclimb.

The present invention is based on a metal physics description of thebehaviour of hardened (martensite or bainite) steels. Hardened steelscan, from a metal physics point of view, be characterised as beingnon-equilibrium steel (at equilibrium all steels are soft). Suchmaterials, therefore, behave differently than softer steels. Sincefatigue is a result of accumulated damage, induced by incrementalmicro-plastic deformation in each load cycle, the key to improvedpredictability lies in understanding the micro-plastic behaviour of hardsteels.

While plastic deformation in softer steels is controlled by onedeformation mechanism, dislocation glide, or micro-yielding, plasticdeformation in hard steels, in their non-equilibrium state, may beinduced by two different mechanisms, dislocation glide and dislocationclimb. The first deformation mechanism is only active above a giventhreshold stress level (the micro-yield limit), while the latter one is,although strongly stress dependent, active at all stress levels, notexcluding the existence of a lower threshold stress level below whichthe climb mechanism does not occur. The dislocation climb mechanism isgoverned by diffusion processes and the fatigue response, therefore,also becomes strongly influenced by temperature, time and internal (hoopand residual) stresses and will therefore also be influenced by therunning speed.

There are two classes of residual stresses. The ones that are inducedduring the manufacturing process and that thus are present from thestart of the fatigue process (initial residual stresses), and residualstresses that develop (evolve) in the surface and/or subsurface materialduring the RCF process as a result of different damage processes. Thecumulative plastic strain damage is likely to dominate. Examples ofcontributing mechanisms to the residual stress evolution are:

-   -   Shakedown, induced by either classic yielding (dislocation        glide) or by a primary creep like deformation process        (dislocation climb+glide). This damage occurs during the early        part of the fatigue process (typically less than one percent of        the fatigue life).    -   Transformation of retained austenite (when applicable) to        martensite or bainite like products (volume increase).    -   Volume changes of the matrix due to accumulation of crystal        defects and due to microstructural changes, followed by:    -   Continuous cumulative plastic strain damage via the        here-discussed (secondary) creep like fatigue damage process        (climb+glide).    -   Microstructural recovery, leading to a partial relaxation of the        residual stress field.

The residual stresses must (just like the load-induced and damagegenerating dynamic (cyclic) contact stress field) be described as athree-dimensional stress tensor that also varies over time, that is, itis also dynamic (evolving), but on a longer time-scale than thecontact-induced stress field. It should also be clear that the residualstress field (tensor), in combination with the hoop stress field(tensor) resulting from interference fitting of inner and outer rings ofbearings, or from centripetal forces induced by rotating components, andother superimposed structural stress components. All these variousstress fields of different origins, including also the dynamic stressfield from the actions of the rolling contact, contribute to theoverall, highly dynamic, stress field tensor. From this stress tensor adeviatoric stress field and a normal stress field can be derived. Herethe deviatoric stress field drives the fatigue damage process, while thenormal stress field influences the rate by which thediffusion-controlled fatigue damage process precedes.

A foundation of the present invention is that the problem of fatigue andfactors underlying fatigue are not classic plastic yielding (that isgoverned by dislocation glide), but a low temperature creep mechanism(that is governed by dislocation climb, itself being rate controlled byiron self-diffusion), rules the fatigue damage process. This lattermechanism is inherently (like all other kinetically controlled chemicaland metallurgical processes) temperature dependent and time dependent.

Fatigue exposed components made of hardened and low-temperature temperedsteels typically fail due to crack initiation from various defects. Inrespect to rolling contact fatigue, these defects are present either atthe raceway surface (indentations from handling damage or mounting,denting from contaminated running or surface damage induced fromimproper lubrication, etc.) or within the material, that is, subsurfacedefects like non-metallic inclusions, pores, pre-existing crack, etc.Defects like these act as local stress raisers leading to a locallyaccelerated fatigue damage. The shear stress driven and thermallyactivated fatigue damage processes discussed in this document thereforeoccur at a higher rate in the steel matrix adjacent to the defects. Thisresults in that the material, at some point in time, will fail locallyat these highly stressed points, leading to crack initiation. From thispoint in time, the fatigue damage process will change to become one ofcrack propagation till failure (spalling).

In FIG. 1 a device 1 suitable for executing the methods according topresent invention is given. It comprises a processor 3 for executing themethods, and input/output means 5, such as a mouse or a keyboard. In anembodiment, it comprises data communication capabilities 7 for receivingand transmitting metal object data. It may also comprise a screen 9and/or a printer 11 for outputting results from the execution of themethods according to the present invention.

The fatigue test described here is run at high contact pressures, higherthan those usually used in bearing applications. The rationale behindthis is that the resulting subsurface plastic deformation, which can beobserved as an evolving groove at the raceway surface, represents thedamage that occur locally at stress raising defects like surface dentsor subsurface defects, such as non-metallic inclusions, under typicalapplication conditions.

The surface groove formation is the result of complex processes, wherethe micro-plastic behaviour is likely to play a central role, but wherealso other deformation mechanisms and the geometry changes of thecontact, induced by the subsurface deformation, etc., also contribute.The grooving model described here describes two contributing parts: Theshakedown effect that occurs early in the rolling contact fatigueexposure and which will here be assumed to be cycle independent(immediate); and: The cycle dependent, gradually evolving, groovingmechanism resulting from the subsurface micro-plasticity processes thatare described here by the creep-like fatigue damage mechanism.

In terms of shakedown strain damage, the plastic strain, γ_(SD), duringthe shakedown step is described using power-law relation (the Ludwikrelation)

γ_(SD) =K< T−T _(u)>^(m)

where K is a material constant, T is the shear stress amplitude, τ_(u)is a threshold shear stress level that must be exceeded to induceplasticity and m is the shear stress exponent for the shakedownmechanism. The arrow bracket indicates that if the argument is negativethe result is zero.

In terms of steady-state strain damage, the cyclic plastic damage,γ_(N), is modelled as follows (under constant f, temperature and shearstress amplitude).

γ_(N) =A _(N) <T−T _(u)>^(c) e ^((−(Q−ΔVσ)/RT)) N/f, where

A_(N) is a material constant, c is the shear stress exponent, Q₀ is theactivation energy for the diffusion controlled micro-plastic strainmechanism in absence of internal stress, ΔV is a material constant, σ isthe hydrostatic stress state resulting from acting normal internalstresses, N is the number of load cycles (or revolutions), f is theloading frequency (or rotational speed), R is the universal gas constantand T is the local absolute operating temperature. Here, the quotientN/f equals the total running time (t) that is proportional to the“cumulative time under stress” during the rolling contact fatigueexposure.

The core of the model constitutes a “state variable”, that is, a givenvalue of such a variable corresponds to a given micro-plastic damage,independent on which combination of τ, T, t (or N/f) and σ, used toreach the value of this state variable. The state variable may bewritten:

P _(N) =<p ₀ −p _(u)>^(c) e ^((−(Q−ΔVσ)/RT)) N/f,

where the shear stress parameters have been replaced by the maximumHertzian contact pressure (p₀) and a threshold contact pressure (p_(u)),respectively.

Below, two examples of alternative grooving models are shown. Thecumulative strain damage for the shakedown and the cycle dependentdamage, γ_(sd) and γ_(N), respectively, are used as arguments in apower-law relation:

G=(a′·γ _(sd) +b′·γ _(N))^(e′)

An alternative relation is given below, where the difference incharacter between the shakedown and steady-state strain damage processesis acknowledged by splitting the relation into a direct dependence ofthe cycle independent shakedown strain and a power-law relationdescribing the influence of the steady-state strain damage:

G=a″·γ _(sd) +b″·γ _(N) ^(e″)

In these relations, the first term accounts for the cycle independentgroove formation and the second term accounts for the time or load cycledependent groove development (sometimes called “ratchetting”). Theconstants a′, b′ and e′, and a″, b″ and e″, respectively, are regressionconstants and where the exponents account for the expected non-linearitybetween the groove depth and the plastic strain due to the groovegeometry changes (changing contact geometry, etc.) and other less welldefined influences.

The equations above give two different forms of the grooving model. Boththese (and other relations) have been assessed in the development of theprocedure for the evaluation of groove data. On fitting the experimentaldata to the selected grooving relation a somewhat modified form of thesecond equation is used from practical considerations:

G=a·

p ₀ −p _(u)

^(m) +b·P _(N) ^(e)

where also the shear stress parameters in the shakedown damage relationhave been replaced by the maximum Hertzian contact pressure and athreshold contact pressure, respectively, and where the constants a, band e are used as regression constants. The physically based materialparameters (p_(u), m, Q₀, ΔV and c), together with the regressionconstants, can be evaluated from the experimental information usingmulti-variable least-square regression analysis.

The grooving model allows also separating the initial (shakedown)damage, and the cyclic or fatigue induced damage. These parameters giveadditional valuable information on the behaviours of different materialvariants as basis for decisions on selecting material and processingroutes for given applications.

A rig 120 usable when determining values of those constants isschematically shown in FIG. 6. The rig 120 allows running idealisedrolling contact fatigue (RCF) tests where essentially only the steelmatrix response to the RCF conditions are evaluated. In an embodiment,the specimen is a cylindrical roller 122 (diameter 18 mm and length 30mm), which is exposed to near point contacts by two ceramic (Si₃N₄)balls 124 (diameter 19 mm), running along the same track on the rollercircumference, giving two stress cycles per specimen revolution. Also,lubrication means 126 for lubricating the near point contacts is alsoprovided. Three bearings 126 are provided to support the balls 124 and anon-driven wheel 128 supports the specimen 122.

This allows controlling closely the operating conditions, allowingvarying contact pressure, varying temperature and varying rotationalspeed. Full film lubrication is maintained at all times. The fatigueresponse of the steel matrix can be evaluated using different techniqueslike metallography (optical and electron microscopy) and X-raytechniques, etc., methods that can be characterised as “indirect”. Inthe method described here a more direct method of determining thecumulated plastic damage is applied, namely recording the grooveformation at the raceway surface, resulting from the subsurfacesmall-scale plastic damage during the RCF exposure.

A typical test programme for a material of interest consists of a testmatrix involving a number of experiments usually run at constant speedand at varying contact pressure levels (at least two) and varyingtemperature (at least two levels). This allows evaluating the basicmaterial parameters, or constants, including p_(u), m, Q₀, and c. Ifalso the material constant ΔV should be evaluated, additionalexperiments with varying internal stress levels such as (tensile) hoopstress (for example obtained by use of a compound roller with a shrinkfitted shell on a roller core) or (usually compressive) residual stress(introduced during manufacturing of the specimen), have to be run (atleast two internal stress levels have to be introduced). For each of theselected test conditions the evolving surface groove is evaluated usingsurface profiling techniques and a defined profile parameter (forexample, groove shoulder to groove bottom or groove depth below theoriginal surface) is defined to represent the groove depth. Thisparameter is measured either in-situ, using on-line interferometry, orintermittently for different exposure times, ranging from short (secondsor minutes) to long (hours or days).

In FIG. 3, a diagram indicating the relation between subsurface plasticfatigue damage observed in the form of a surface groove, plotted versusnumber of load cycles, and temperature, is given. This is an example ofthe correlation between the grooving model and experimental data fromthe testing of martensitically induction hardened, unalloyed, mediumcarbon bearing steel. The following set of material constants werefound, as a result of the simultaneous multi-variable regressionanalysis of all data points (n=24):

m=2.5p_(u)=580 MPac=16.3

Q₀=100 500 J/mol

In this case the ΔV value could not be evaluated since all tests wererun without changing the internal stress parameter. The groove modelfitting parameters took here the values: a=2.44·10⁻¹⁰, b=1.48·10⁻¹³ ande=0.254, with an overall correlation coefficient r²=0.986. The diagramshows the grooving response after testing at two levels of contactpressure, 3.2 and 4.9 GPa, and at two temperatures, 65 and 100° C.Markers represent measured groove depths and the curves are the resultof a simultaneous, multi-variable regression analysis of all data pointsshown (n=24, r²=0.986). Also applicable to other figures, (Exp) denotesexperimental data and (Mod) denotes data as originated from the groovingmodel.

In FIGS. 4A and 4B, diagrams indicating the relation between subsurfaceplastic fatigue damage observed in the form of a surface groove, plottedversus number of load cycles, and temperature, are given. This is anexample of the correlation between the grooving model and experimentaldata from the testing of martensitically through hardened, low-alloyed,high-carbon bearing steel. The following set of material constants werefound as a result of the simultaneous multi-variable regression analysisof all data points (n=40):

-   -   m=10    -   p_(u)=1200 MPa    -   c=13.6    -   Q₀=135 000 J/mol

In this case the ΔV value could not be evaluated since all tests wererun without changing the internal stress parameter. The groove modelfitting parameters took here the values: a=4.13·10⁻³⁷, b=9.55·10⁻¹⁰ ande=0.258, with an overall correlation coefficient r²=0.979. The diagramsshow the grooving response after testing at a range of contact pressuresand at two temperatures, 65 and 100° C. Markers represent measuredgroove depths and the curves are the result of a simultaneous,multi-variable regression analysis of all data points shown (n=40,r²=0.979).

In FIG. 5, an example of the correlation between the grooving model andexperimental grooving data of martensitically hardened, chromium andvanadium alloyed tool steel of bearing quality is shown. The followingset of material constants were found for this secondary hardened toolsteel, as a result of the simultaneous multi-variable regressionanalysis of all data points (n=35):

-   -   m=6    -   p_(u)=2500 MPa    -   c=17.2    -   Q₀=106 000 J/mol

In this case the ΔV value could not be evaluated since all tests wererun without changing the internal stress parameter. The groove modelfitting parameters took here the values: a=9.34·10⁻²², b=4.16·10⁻⁷ ande=0.132, with a correlation coefficient of r²=0.988. The diagram showsthe grooving response after testing at two levels of contact pressure,4.0 and 5.0 GPa, and at two temperatures, 75 and 100° C. Markersrepresent measured groove depths and the curves are the result of asimultaneous, multi-variable regression analysis of all data pointsshown (n=35, r²=0.988).

1. A method of indicating fatigue damage rate of a hardened metal objectin relation to load cycles, N, exerted on the hardened metal object,comprising the step of: calculating the fatigue damage rate based on aneffective activation energy parameter for the dislocation climb process,Q, shear stress amplitude, τ, the absolute local temperature of thehardened metal object, T, and load frequency, f.
 2. The method accordingto claim 1, wherein the step of calculating includes calculating thefatigue damage rate according todγ/dN=A<τ−τ _(u)>^(c) e ^((−kQ/RT)) /f, where: A isA₀(H_(Vref)/H_(V))^(d), where A₀ is a constant greater than zero andlesser than 10⁻⁸, H_(Vref) is the Vickers hardness for a referencemetal, H_(V) is the Vickers hardness for the hardened metal object,<τ−τ_(u)> is zero for τ≦τ_(u) and τ−τ_(u) for τ>τ_(u), where τ_(u) isthe fatigue limit for the hardened metal object, c is a constant in theinterval 6 to 22, d is a constant in the interval 6 to 22, k is aconstant between 0.50 and 1.50, T is the absolute temperature of thehardened metal object at the point of contact, and R is the universalgas constant.
 3. The method according to claim 1, wherein the step ofcalculating includes calculating the fatigue damage rate according todγ/dt=A<τ−τ _(u)>^(c) e ^((−kQ/RT)), where: A is A₀(H_(Vref)/H_(V))^(d), where A₀ is a constant greater than zero andlesser than 10⁻⁸, H_(Vref) is the Vickers hardness for a referencemetal, H_(V) is the Vickers hardness for the hardened metal object,<τ−τ_(u)> is zero for τ≦τ_(u) and τ−τ_(u) for τ>τ_(u), where τ_(u) isthe fatigue limit for the hardened metal object, c is a constant in theinterval 6 to 22, d is a constant in the interval 6 to 22, k is aconstant between 0.50 and 1.50, T is the absolute temperature of thehardened metal object at the point of contact, and R is the universalgas constant.
 4. The method according to claim 1, wherein thetemperature, T, is in the interval of zero degrees Celsius to 250degrees Celsius.
 5. The method according to claim 1, wherein thetemperature, T, is in the interval of 15 degrees Celsius to 200 degreesCelsius.
 6. The method according to claim 1, wherein the temperature, T,is lesser than 0.4T_(m), where T_(m) is the absolute melting temperatureof the hardened metal object.
 7. The method according to claim 1,further comprising the step of calculating the effective activationenergy parameter for the dislocation climb process, Q, according toQ=Q ₀ −ΔVσ, where ΔV is a material constant, and σ is the normal stressfield.
 8. The method according to claim 7, wherein σ is the hydrostaticstress.
 9. The method according to claim 8, wherein σ is calculatedaccording toσ=(σ_(xx)+σ_(yy)+σ_(zz))/3, where σ_(xx), σ_(yy), σ_(zz) are the normalstress components.
 10. A method of indicating fatigue damage, γ, of ahardened metal object at a temperature substantially corresponding tothe operating conditions of the hardened metal object and under constantstress amplitude, comprising the step of: calculating the fatiguedamage, γ, based on effective activation energy parameter for thedislocation climb process, Q, shear stress amplitude, τ, the absolutelocal temperature of the hardened metal object, T, load frequency, f,and number of load cycles, N, exerted on the hardened metal object. 11.The method according to claim 10, wherein the step of calculatingincludes calculating γ according toγ=A<τ−τ _(u)>^(c) e ^((−kQ/RT)) N/f, where A is A₀(H_(Vref)/H_(V))^(d),where A₀ is a constant greater than zero and lesser than 10⁻⁸, H_(Vref)is the Vickers hardness for a reference metal, H_(V) is the Vickershardness for the hardened metal object, <τ−τ_(u)> is zero for τ≦τ_(u)and τ−τ_(u) for τ>τ_(u), where τ_(u) is the fatigue limit for thehardened metal object, c is a constant in the interval 6 to 22, d is aconstant in the interval 6 to 22, k is a constant between 0.50 and 1.50,T is the absolute temperature of the hardened metal object at the pointof contact, and R is the universal gas constant.
 12. The methodaccording to claim 10, wherein the step of calculating includescalculating γ according toγ=A<τ−τ _(u)>^(c) e ^((−kQ/RT)) t, where: A is A₀(H_(Vref)/H_(V))^(d),where A₀ is a constant greater than zero and lesser than 10⁻⁸, H_(Vref)is the Vickers hardness for a reference metal, H_(V) is the Vickershardness for the hardened metal object, <τ−τ_(u)> is zero for τ≦τ_(u)and τ−τ_(u) for τ>τ_(u), where τ_(u) is the fatigue limit for thehardened metal object, c is a constant in the interval 6 to 22, d is aconstant in the interval 6 to 22, k is a constant between 0.50 and 1.50,T is the absolute temperature of the hardened metal object at the pointof contact, and R is the universal gas constant.
 13. The methodaccording to claim 10, wherein the temperature, T, is in the interval ofzero degrees Celsius to 250 degrees Celsius.
 14. The method according toclaim 10, wherein the temperature, T, is in the interval of 15 degreesCelsius to 200 degrees Celsius.
 15. The method according to claim 10,wherein the temperature, T, is lesser than 0.4T_(m), where T_(m) is theabsolute melting temperature of the hardened metal object.
 16. Themethod according to claim 10, further comprising the step of calculatingthe effective activation energy parameter for the dislocation climbprocess, Q, according toQ=Q ₀ −ΔVσ, where ΔV is a material constant, and σ is the normal stressfield.
 17. The method according to claim 16, wherein σ is thehydrostatic stress.
 18. The method according to claim 17, wherein σ iscalculated according toσ=(σ_(xx)+σ_(yy)+σ_(zz))/3, where σ_(xx), σ_(yy), σ_(zz) are the normalstress components.
 19. A method of indicating at least one of aneffective activation energy parameter for the dislocation climb process,Q, shear stress amplitude, τ, the absolute local temperature of thehardened metal object, T, load frequency, f, and number of load cycles,N, exerted on the hardened metal object, at a temperature substantiallycorresponding to the operating conditions of the hardened metal objectand under constant stress amplitude, comprising the step of calculating:N=Cf/(<τ−τ_(u)>^(c) e ^((−kQ/RT))), where: C=C₀(H_(V)/H_(Vref))^(d),where C₀ is a calibration constant representing operating conditions fora reference metal object having a known fatigue life in terms ofestimated maximum number of load cycles, H_(Vref) is the Vickershardness for a reference metal and H_(V) is the Vickers hardness for thehardened metal object, <τ−τ_(u)> is zero for τ≦τ_(u) and τ−τ_(u) forτ>τ_(u), where τ_(u) is the fatigue limit for the hardened metal object,c is a constant in the interval 6 to 22, d is a constant in the interval6 to 22, k is a constant between 0.50 and 1.50, T is the absolutetemperature of the hardened metal object at the point of contact, and Ris the universal gas constant.
 20. The method according to claim 19,wherein the temperature, T, is in the interval of zero degrees Celsiusto 250 degrees Celsius.
 21. The method according to claim 19, whereinthe temperature, T, is in the interval of 15 degrees Celsius to 200degrees Celsius.
 22. The method according to claim 19, wherein thetemperature, T, is lesser than 0.4T_(m), where T_(m) is the absolutemelting temperature of the hardened metal object.
 23. The methodaccording to claim 19, further comprising the step of calculating theeffective activation energy parameter for the dislocation climb process,Q, according toQ=Q ₀ −ΔVσ, where ΔV is a material constant, and σ is the normal stressfield.
 24. The method according to claim 23, wherein σ is thehydrostatic stress.
 25. The method according to claim 24, wherein σ iscalculated according toσ=(σ_(xx)+σ_(yy)+σ_(zz))/3, where σ_(xx), σ_(yy), σ_(zz) are the normalstress components.
 26. A computer program product loadable into theinternal memory of a computer, comprising software code portionsexecutable on a computer for performing at least one of the steps ofcalculating a fatigue damage rate based on an effective activationenergy parameter for the dislocation climb process, Q, shear stressamplitude, τ, the absolute local temperature of the hardened metalobject, T, and load frequency, f so as to indicate fatigue damage rateof a hardened metal object in relation to load cycles, N, exerted on thehardened metal object; and calculating fatigue damage, γ, based oneffective activation energy parameter for the dislocation climb process,Q, shear stress amplitude, τ, the absolute local temperature of thehardened metal object, T, load frequency, f, and number of load cycles,N, exerted on the hardened metal object so as to indicate the fatiguedamage, γ, of a hardened metal object at a temperature substantiallycorresponding to the operating conditions of the hardened metal objectand under constant stress amplitude.
 27. (canceled)